Problem: Solve for $x$ and $y$ using substitution. ${-2x-4y = 12}$ ${y = -x-5}$
Explanation: Since $y$ has already been solved for, substitute $-x-5$ for $y$ in the first equation. ${-2x - 4}{(-x-5)}{= 12}$ Simplify and solve for $x$ $-2x+4x + 20 = 12$ $2x+20 = 12$ $2x+20{-20} = 12{-20}$ $2x = -8$ $\dfrac{2x}{{2}} = \dfrac{-8}{{2}}$ ${x = -4}$ Now that you know ${x = -4}$ , plug it back into $\thinspace {y = -x-5}\thinspace$ to find $y$ ${y = -}{(-4)}{ - 5}$ $y = 4 - 5$ $y = -1$ You can also plug ${x = -4}$ into $\thinspace {-2x-4y = 12}\thinspace$ and get the same answer for $y$ : ${-2}{(-4)}{ - 4y = 12}$ ${y = -1}$